IMAT Chemistry · Organic Chemistry

Isomerism: Structural Isomers, Cis/Trans and Chirality

Isomers have the same molecular formula but a different arrangement of atoms, either in what is bonded to what (structural) or in how it is arranged in space (stereo).

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Why this matters

Isomers were the favourite topic of the Cambridge papers, which asked 'which of these are structural isomers' in most years from 2013 to 2022. The ministry papers asked for isomers of hexanoic acid in 2023 and, in 2026, which families a given formula with one oxygen could belong to.

Concept 1 of 3: Structural isomers: chain, position and functional group

With the same set of atoms you can build different skeletons, put a group on a different carbon, or even build a different family. A ring uses up hydrogens exactly like a double bond, so a cyclic compound and an open-chain alkene can be isomers.

Definition

Isomers have the same molecular formula. Structural isomers differ in which atoms are bonded to which.

Chain isomers: different skeletons (pentane, 2-methylbutane, 2,2-dimethylpropane are the three $\mathrm{C_5H_{12}}$ ).
Position isomers: same group on a different carbon (propan-1-ol and propan-2-ol).
Functional group isomers: different families with one formula. Alcohol and ether; aldehyde and ketone; carboxylic acid and ester; alkene and cycloalkane.
A formula with one O and DoU 1 (like $\mathrm{C_4H_8O}$ ) can be an aldehyde, a ketone, or an alcohol or ether that has a C=C or a ring.
Isomers usually have different physical properties (boiling point, solubility), and functional group isomers different chemistry too.
Test: write both molecular formulas and compare. Then check the two drawings are not the same molecule turned round.

Worked example

How many structural isomers have the formula

\mathrm{C_4H_{10}O}

? Name them.

Practice this conceptself-check · 4 quick reps

Isomers need not have similar physical properties

The definition only requires the same molecular formula and a different structure. Ethanol boils at about 78 °C while its isomer dimethyl ether boils at about −24 °C. A statement that isomers must have similar properties is false.

A formula with one oxygen and one degree of unsaturation is not only a carbonyl compound

\mathrm{C_4H_8O}

can be butanal or butanone, but also an alcohol with a C=C (but-3-en-1-ol) or a ring (cyclobutanol), or a cyclic ether. Options that rule out the alcohol forget that a ring or C=C can supply the missing two hydrogens.

Concept 2 of 3: Cis/trans (geometric) isomerism around a C=C

Groups on a single bond can spin round, but a double bond is locked by its π bond. So two groups on the carbons of a C=C can be fixed on the same side or on opposite sides. That gives two different molecules, but only if each carbon has two different things attached.

Definition

Stereoisomers have the same atoms bonded in the same order, but a different arrangement in space.

Cis/trans (also called geometric or E/Z) isomerism needs restricted rotation (a C=C, or a ring) and two different groups on each carbon of the double bond.
Cis: the matching groups on the same side. Trans: on opposite sides.
If either carbon of the C=C carries two identical groups (two H, two $\mathrm{CH_3}$ ), there is no cis/trans isomerism.
Cis and trans isomers have different physical properties, such as boiling point and melting point.

Compound	Groups on the two C=C carbons	Cis/trans isomers?
But-2-ene $\mathrm{CH_3CH{=}CHCH_3}$	H and $\mathrm{CH_3}$ ; H and $\mathrm{CH_3}$	Yes
But-1-ene $\mathrm{CH_2{=}CHCH_2CH_3}$	H and H; H and $\mathrm{C_2H_5}$	No: carbon 1 has two H
2-methylbut-2-ene $\mathrm{(CH_3)_2C{=}CHCH_3}$	$\mathrm{CH_3}$ and $\mathrm{CH_3}$ ; H and $\mathrm{CH_3}$	No: carbon 2 has two $\mathrm{CH_3}$
1,2-dichloroethene $\mathrm{CHCl{=}CHCl}$	H and Cl; H and Cl	Yes
1,1-dichloroethene $\mathrm{CCl_2{=}CH_2}$	Cl and Cl; H and H	No

Practice this conceptself-check · 3 quick reps

A C=C is needed for cis/trans, but it is not enough

Every alkene has a C=C, but only some have cis/trans isomers. If either double-bond carbon carries two identical groups, swapping sides gives the same molecule. Check both carbons separately.

Concept 3 of 3: Chirality: chiral carbons and optical isomers

Your left and right hands are mirror images, but you cannot lay one exactly on top of the other. A carbon with four different groups is the same: it and its mirror image are two different molecules. They behave identically in almost every way, which is why they are hard to tell apart.

Definition

A chiral centre (asymmetric carbon) is an sp³ carbon bonded to four different groups.
A molecule with one chiral centre exists as two enantiomers (optical isomers): non-superimposable mirror images.
Enantiomers have the same boiling point, melting point, density and solubility. They rotate plane-polarised light by the same angle in opposite directions.
A 50:50 mixture of two enantiomers is a racemic mixture and shows no overall rotation.
Enzymes are chiral, so they often act on only one enantiomer. All amino acids except glycine are chiral; proteins use the L forms.
A molecule with $n$ chiral centres has at most $2^n$ stereoisomers.

Maximum number of stereoisomers

N_{\max} = 2^{n}

$n$ number of chiral centres
$N_{\max}$ upper limit; symmetric molecules can have fewer

Worked example

Find the chiral centres in 3-chlorobutan-2-ol,

\mathrm{CH_3CH(OH)CH(Cl)CH_3}

, and the maximum number of stereoisomers.

Practice this conceptself-check · 4 quick reps

Enantiomers have the same physical properties

Boiling point, melting point, density and solubility are identical for the two enantiomers. They differ only in the direction they rotate plane-polarised light and in how they interact with other chiral molecules, such as enzymes and receptors.

A carbon in a double bond cannot be a chiral centre

A chiral centre needs four different groups on four single bonds, so it must be sp³. A C=C or C=O carbon is joined to only three atoms and is never chiral.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Chirality: chiral carbons and optical isomers
Maximum number of stereoisomers
$N_{\max} = 2^{n}$

Reference tables (1)

Cis/trans (geometric) isomerism around a C=C5 rows

Compound	Groups on the two C=C carbons	Cis/trans isomers?
But-2-ene $\mathrm{CH_3CH{=}CHCH_3}$	H and $\mathrm{CH_3}$ ; H and $\mathrm{CH_3}$	Yes
But-1-ene $\mathrm{CH_2{=}CHCH_2CH_3}$	H and H; H and $\mathrm{C_2H_5}$	No: carbon 1 has two H
2-methylbut-2-ene $\mathrm{(CH_3)_2C{=}CHCH_3}$	$\mathrm{CH_3}$ and $\mathrm{CH_3}$ ; H and $\mathrm{CH_3}$	No: carbon 2 has two $\mathrm{CH_3}$
1,2-dichloroethene $\mathrm{CHCl{=}CHCl}$	H and Cl; H and Cl	Yes
1,1-dichloroethene $\mathrm{CCl_2{=}CH_2}$	Cl and Cl; H and H	No

Watch out for (5)

Isomers need not have similar physical properties
→ Structural isomers: chain, position and functional group
A formula with one oxygen and one degree of unsaturation is not only a carbonyl compound
→ Structural isomers: chain, position and functional group
A C=C is needed for cis/trans, but it is not enough
→ Cis/trans (geometric) isomerism around a C=C
Enantiomers have the same physical properties
→ Chirality: chiral carbons and optical isomers
A carbon in a double bond cannot be a chiral centre
→ Chirality: chiral carbons and optical isomers

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